This grant is the continuation of a collaborative multi-disciplinary study of the mechanical initiation of injury to soft tissue in the kidney and of damage to tissue analogs by ESWL shock waves. Experiments are carried out in a laboratory lithotripter of our own design that mimics the Dornier HM3 electrohydraulic lithotripter. Finite-difference numerical solutions of the Euler equations are obtained for focusing shock waves interacting with tissue and kidney stones. Cooperative research is carried out with the other Projects of this Program Project Grant to advance the objectives of the Grant. The aims of this Project are: I. Extend the dose criterion developed in our previous work on the cavitation-free failure of planar membranes to more complex weak mechanical structures and, in collaboration with Project 2, to in vitro cell cultures. Included in this aim is the development of a tissue phantom which reliably mimics the shock-wave scattering properties of soft tissue, development PVDF transducer arrays, investigation of membrane material/cavitation-free host fluid combinations and thin-membrane cylindrical structures for damage studies, and collaborations with Projects 1 and 2 to develop a physically-based quantitative definition of ESWL dose. II. Initiate a new effort in Project 4 to demonstrate the mechanisms of kidney stone comminution by ESWL. Included in this aim is utilization of the Hopkinson bar technique to characterize the failure dynamics of real and phantom calculi, and development of a stone phantom which faithfully mimics the failure models of kidney stones. III. Develop numerical methods for solving the exact Euler equations of motion. Included in this aim is adaptation of the Amrita problem-solving environment to shock wave focusing problems, calculation of shock wave focusing by an ellipse in uniform and non-uniform media, and calculation of wave shapes and compressive stresses induced by impingement of a shock wave on a theoretical calculus. The hypothesis that the above aims are designed to test include: 1. A quantitative definition of ESWL dose, based on the physical properties of waves and tissue, can be developed to quantify the mechanical input of ESWL to tissue. 2. Comminution of kidney stones in ESWL occurs under shock compression by dynamic fatigue. 3. Accurate numerical calculations of shock pressure and wave geometry during shock wave focusing can be used with experimental data to elucidate mechanisms of stone comminution and tissue injury.